Rough paths


This page is dedicated to gather informations on rough paths theory.

bib file of the bibliography below.



  • Peter K. Friz (Cambridge) [www]
  • Massimiliano Gubinelli (Orsay) [www]



  1. M. Gubinelli. Ramification of rough paths. 2006. (arXiv)
  2. M. Gubinelli. Rough solutions of the periodic Korteweg-de Vries equation. 2006. (arXiv)
  3. P. Friz and N. Victoir. The burkholder-davis-gundy inequality for enhanced martingales. 2006. (arXiv)
  4. P. Friz and N. Victoir. Euler estimates for rough differential equations. 2006.
  5. P. Friz and N. Victoir. A note on the notion of geometric rough paths. 2004.
  6. P. Friz and N. Victoir. On uniformly subelliptic operators and stochastic area. 2006. (arXiv)
  7. D. Feyel and A. de La Pradelle. Curvilinear integrals along enriched paths. 2005.



  1. T. Lyons and Z. Qian. System Control and Rough PathsOxford University Press, 2002.



  1. L. Coutin and Z. Qian. Stochastic differential equations for fractional Brownian motions. C. R. Acad. Sci. Paris Sér. I Math.331(1):75–80, 2000.
  2. L. Coutin and Z. Qian. Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields122(1):108–140, 2002.
  3. A. M. Davie. Differential equations driven by rough signals: an approach via discrete approximation. 2003.
  4. H. Bessaih, M. Gubinelli, and F. Russo. The evolution of a random vortex filament. Ann. Probab.33(5):1825–1855, 2005. (arXiv)
  5. J. G. Gaines and T. Lyons. Random generation of stochastic area integrals. SIAM J. Appl. Math.54(4):1132–1146, 1994.
  6. J. G. Gaines and T. Lyons. Variable step size control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math.57(5):1455–1484, 1997.
  7. B. Hambly and T. Lyons. Uniqueness for the Signature of a Path of Bounded Variation. 2002.
  8. B. Hambly and T. Lyons. Stochastic area for Brownian motion on the Sierpinski gasket. Ann. Probab.26(1):132–148, 1998.
  9. M. Ledoux, T. Lyons, and Z. Qian. Lévy area of Wiener processes in Banach spaces. Ann. Probab.30(2):546–578, 2002.
  10. M. Ledoux, Z. Qian, and T. Zhang. Large deviations and support theorem for diffusion processes via rough paths. 2002.
  11. A. Lejay. Stochastic differential equations driven by a processes generated by divergence form operators. 2002.
  12. A. Lejay. An introduction to rough paths. 2002.
  13. X. D. Li and T. Lyons. Smoothness of the Itô map on p-rough path spaces (I): 1 < p < 2. 2002.
  14. T. Lyons. Differential equations driven by rough signals. I. An extension of an inequality of L. C. Young. Math. Res. Lett.1(4):451–464, 1994.
  15. T. Lyons. The interpretation and solution of ordinary differential equations driven by rough signals. In Stochastic analysis (Ithaca, NY, 1993)pages 115–128. Amer. Math. Soc., Providence, RI, 1995.
  16. T. Lyons. Differential equations driven by rough signals. Rev. Mat. Iberoamericana14(2):215–310, 1998.
  17. T. Lyons and A. Lejay. On the importance of the Lévy area for systems controlled by converging stochastic processes. application to homogenization. 2002.
  18. T. Lyons and Z. Qian. System Control and Rough PathsOxford University Press, 2002.
  19. T. Lyons and Z. Qian. Calculus for multiplicative functionals, Itô’s formula and differential equations. In Itô’s stochastic calculus and probability theorypages 233–250. Springer, Tokyo, 1996.
  20. T. Lyons and Z. Qian. A class of vector fields on path spaces. J. Funct. Anal.145(1):205–223, 1997.
  21. T. Lyons and Z. Qian. Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Probab. Theory Related Fields109(4):539–570, 1997.
  22. T. Lyons and Z. Qian. Flow equations on spaces of rough paths. J. Funct. Anal.149(1):135–159, 1997.
  23. T. Lyons and Z. Qian. Calculus of variation for multiplicative functionals. In New trends in stochastic analysis (Charingworth, 1994)pages 348–374. World Sci. Publishing, River Edge, NJ, 1997.
  24. T. Lyons and Z. Qian. Flow of diffeomorphisms induced by a geometric multiplicative functional. Probab. Theory Related Fields112(1):91–119, 1998.
  25. T. Lyons and L. Stoica. On the limit of stochastic integrals of differential forms. In Stochastic processes and related topics (Siegmundsberg, 1994)pages 61–66. Gordon and Breach, Yverdon, 1996.
  26. T. Lyons and L. Stoica. The limits of stochastic integrals of differential forms. Ann. Probab.27(1):1–49, 1999.
  27. T. Lyons and N. Victoir. Cubature on Wiener space. 2002.
  28. T. Lyons and O. Zeitouni. Conditional exponential moments for iterated Wiener integrals. Ann. Probab.27(4):1738–1749, 1999.
  29. A. Lejay. An introduction to rough paths. In Séminaire de Probabilités XXXVIIvolume 1832 of Lecture Notes in Math.pages 1–59. Springer, Berlin, 2003.
  30. M. Gubinelli. Controlling rough paths. J. Funct. Anal.216(1):86–140, 2004.
  31. P. Friz and N. Victoir. Approximations of the Brownian rough path with applications to stochastic analysis. Ann. Inst. H. Poincaré Probab. Statist.41(4):703–724, 2005.
  32. L. Coutin and A. Lejay. Semi-martingales and rough paths theory. Electron. J. Probab.10:no. 23, 761–785 (electronic), 2005.
  33. E.-M. Sipiläinen. A pathwise view of solutions of stochastic differential equations. PhD thesis, University of Edinburgh, 1993.
  34. D. R. E. Williams. Diffeomorphic flows driven by Lévy processes. 2000.
  35. D. R. E. Williams. Path-wise solutions of stochastic differential equations driven by Lévy processes. Rev. Mat. Iberoamericana17(2):295–329, 2001.
  36. D. R. E. Williams. Solutions of differential equations driven by càdlàg paths of finite p-variation. PhD thesis, Imperial College, London, 1998.
  37. A. Lejay, M. Gubinelli, and S. Tindel. Young integrals and SPDEs. Pot. Anal.2006. to appear. (arXiv)


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